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(a) Which variable is the respon O X1 O X2 X3

(a) Which variable is the respon O X1 O X2 X3

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Use the following linear regression equation to answer the questions. X1 = 1.5 + 3.6x2 - 7.7x3 + 2.3x4 (a) Which variable is the response variable? O X4 O X2 O 3 Which variables are the explanatory variables? (Select all that apply.) O 3 O X4 O X1 O ×2 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient X, coefficient X4 coefficient (c) If x2 = 4, x3 = 9, and x4 = 10, what is the predicted value for x,? (Use 1 decimal place.) (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope." O If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." O If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope." O If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line.
Transcribed Image Text:Use the following linear regression equation to answer the questions. X1 = 1.5 + 3.6x2 - 7.7x3 + 2.3x4 (a) Which variable is the response variable? O X4 O X2 O 3 Which variables are the explanatory variables? (Select all that apply.) O 3 O X4 O X1 O ×2 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant X2 coefficient X, coefficient X4 coefficient (c) If x2 = 4, x3 = 9, and x4 = 10, what is the predicted value for x,? (Use 1 decimal place.) (d) Explain how each coefficient can be thought of as a "slope" under certain conditions. O If we look at all coefficients together, each one can be thought of as a "slope." O If we hold all explanatory variables as fixed constants, the intercept can be thought of as a "slope." O If we hold all other explanatory variables as fixed constants, then we can look at one coefficient as a "slope." O If we look at all coefficients together, the sum of them can be thought of as the overall "slope" of the regression line.
Suppose x3 and x4 were held at fixed but arbitrary values and x, increased by 1 unit. What would be the corresponding change in x,? Suppose x, increased by 2 units. What would be the expected change in X1? Suppose x, decreased by 4 units. What would be the expected change in x1? (e) Suppose that n = 16 data points were used to construct the given regression equation and that the standard error for the coefficient of x, is 0.307. Construct a 95% confidence interval for the coefficient of x,. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of xɔ is different from zero. (Use 2 decimal places.) t critical + Conclusion O Reject the null hypothesis, there is sufficient evidence that ß, differs from 0. O Reject the null hypothesis, there is insufficient evidence that ß, differs from 0. O Fail to reject the null hypothesis, there is insufficient evidence that B2 differs from 0. O Fail to reject the null hypothesis, there is sufficient evidence that ß, differs from 0. Explain how the conclusion of this test would affect the regression equation. O If we conclude that B, is not different from 0 then we would remove X3 from the model. O If we conclude that ß, is not different from 0 then we would remove X1 from the model. O If we conclude that ß, is not different from 0 then we would remove X4 from the model. O If we conclude that B, is not different from 0 then we would remove X2 from the model.
Transcribed Image Text:Suppose x3 and x4 were held at fixed but arbitrary values and x, increased by 1 unit. What would be the corresponding change in x,? Suppose x, increased by 2 units. What would be the expected change in X1? Suppose x, decreased by 4 units. What would be the expected change in x1? (e) Suppose that n = 16 data points were used to construct the given regression equation and that the standard error for the coefficient of x, is 0.307. Construct a 95% confidence interval for the coefficient of x,. (Use 2 decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 1%, test the claim that the coefficient of xɔ is different from zero. (Use 2 decimal places.) t critical + Conclusion O Reject the null hypothesis, there is sufficient evidence that ß, differs from 0. O Reject the null hypothesis, there is insufficient evidence that ß, differs from 0. O Fail to reject the null hypothesis, there is insufficient evidence that B2 differs from 0. O Fail to reject the null hypothesis, there is sufficient evidence that ß, differs from 0. Explain how the conclusion of this test would affect the regression equation. O If we conclude that B, is not different from 0 then we would remove X3 from the model. O If we conclude that ß, is not different from 0 then we would remove X1 from the model. O If we conclude that ß, is not different from 0 then we would remove X4 from the model. O If we conclude that B, is not different from 0 then we would remove X2 from the model.
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Regression line

x1 = 1.5 + 3.6x2 -7.7x3 + 2.3x4

 

a)
Response variable = x1

Explanatory variables = x2,x3,x4

 

 

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